基于正交距离回归齿面的齿轮误差评定

为了通过测量齿面拓扑轮廓来获取特征线误差,提出了一种基于正交距离回归齿面的误差计算方法。对该方法涉及的实际齿面与理论齿面匹配算法、拓扑轮廓误差的计算与分解及齿面特征线误差的评定算法进行了研究。首先,通过坐标测量方法获取的齿面拓扑数据,建立包含回归齿面参数的非线性方程。然后,求解非线性方程得到回归齿面参数的最优近似解,从而得到与实际齿面匹配的理论齿面,拓扑测量点相对理论齿面的正交距离即为齿面拓扑误差。最后,基于齿轮误差多自由度理论,对实际齿面进行局部自由度及全局自由度回归,进一步分解出齿面的齿廓误差和螺旋线误差。以一标准圆柱直齿轮的齿面拓扑测量点数据为例进行了误差计算,结果显示:计算的结果与直接进行特征线测量的结果差值小于0.5μm,表明提出的基于正交距离回归齿面进行齿轮误差评定的方法是有效的,可以应用于坐标类仪器检测齿轮误差。

Evaluation of gear errors based on orthogonal distance regression gear profile

To obtain the error of gear characterized curves from gear topographic inspection, a method of gear profile orthogonal distance regression was proposed. Some algorithms involved in the method were researched, such as the matching of a real gear profile with a theoretical gear profile, the calculation and decomposition of topographic error and the evaluation of profile character line error. Firstly, topographic points were obtained by coordinate measurement, and the nonlinear equation including parameters of theoretic profile was established. Then, the nonlinear equation was solved to get the optimal parameters of the regression gear profile and to obtain the theoretical gear profile matching with the real gear profile. Here, the orthogonal distances from measuring points to the theoretical gear surface were calculated as the topographic errors. Finally, based on the multi-degrees of freedom theory for gear deviation, the gear profile error and the helix error were evaluated by local degree regression and holistic degree regression. The coordinate measuring points on a cylindrical gear were used as an example for error calculation. The results are well consistent with the characterized curves measurement using a coordinate measuring machine, and the difference is within 0.5μm. These results show that the proposed gear profile orthogonal distance regression is reasonable and effective, and it can be applied to the gear inspection using coordinate measuring machines.